Fluid Properties

Fluid Properties

• Density (ρ) is a measure of mass per volume, with units of kg/m³.
• Example densities: ρair = 1.2 kg/m³, ρwater = 1000 kg/m³, ρHg = 13600 kg/m³.

Specific Weight or Weight Density

• Specific weight represents the force exerted by gravity on unit volume of a fluid.
• It can be used as a characteristic property of a fluid.
• Dimension of Specific Weight = M¹L⁻²T⁻².

Specific Gravity

• Specific gravity is used to define the density of a liquid as compared to the density of an equal volume of water at a specified temperature.
• The temperature used for measurement is usually 4°C, because this temperature allows water to assume its maximum density.
• Specific gravity is a function of temperature.
• Specific gravity of water is 1 at 4°C.
• Hydrometer is used to measure the specific gravity of a liquid.

Bulk Modulus

• Bulk modulus is defined as the ratio of the infinitesimal pressure increase to the resulting decrease of the volume.
• It is a measure of resistance to compressibility of a fluid.
• Unit of Bulk Modulus = N/m² or Pa.
• Dimension of Bulk Modulus = M¹L⁻¹T⁻².

Compressibility (β)

• Compressibility is a measure of the relative volume change of a fluid or solid as a response to pressure change.
• It is the reciprocal of bulk modulus.
• Unit of Compressibility = Pa⁻¹.
• Dimensions of Compressibility = M⁻¹L¹T².

Viscosity

• Viscosity is the property of a fluid that indicates resistance to flow over a surface.
• In case of liquids, viscosity is due to cohesion forces, and in case of gases, viscosity is due to molecular momentum transfer.
• Kinematic viscosity: S.I. unit = m²/s, C.G.S unit = cm²/s = Stoke.
• Dynamic viscosity (μ) or absolute viscosity: S.I. unit = kg/m-s = Pa – s, C.G.S unit = Poise.
• Dimension of Dynamic viscosity (μ) = M¹L⁻¹T⁻¹.
• Dimension of Kinematic viscosity (ν) = M⁰L²T⁻¹.
• Redwood viscometer is used to measure Dynamic viscosity or absolute value of viscosity.

Effect of Temperature and Pressure on Viscosity

• For liquids:
  • If temperature increases: μ and ν decreases.
  • If pressure increases: μ and ν remains same.
• For gases:
  • If temperature increases: μ and ν increases.
  • If pressure increases: μ remains same and ν decreases.

Types of Fluid

• Ideal Fluid:
  • Viscosity is zero, meaning resistance to shearing deformation is zero.
  • No shear stress in the case of an ideal fluid.
  • An ideal fluid is frictionless and incompressible.
  • An ideal fluid has negligible surface tension.
• Newtonian fluid:
  • Follows Newton’s law of viscosity.
  • Examples: water, alcohol, gasoline.
• Non-Newtonian fluid:
  • Does not follow Newton’s law of viscosity.
  • Relation between shear stress and velocity gradient is given as:
  • Time Independent Non-Newtonian fluid:
    • Apparent viscosity is not a function of time.
    • Examples: honey, quick sand, starch solution.
  • Time dependent Non-Newtonian Fluid:
    • Apparent viscosity is a function of time.
    • Examples: Ketchup, paints, sludgy.

Surface Tension

• Surface Tension is the property of a fluid that tries to shrink the fluid into the minimum surface area.
• It exists due to the intermolecular force of attraction (Cohesive force) between the molecules of same fluid.
• Gauge pressure inside a spherical drop, bubble, and liquid jet.
• Due to surface tension only, liquid droplets take the spherical shape because the spherical shape has the smallest surface area for a given volume.

Wetting and Non-Wetting Phenomenon

• Wetting phenomenon:
  • Adhesive force > cohesive force.
  • Angle of contact is less than π/2.
• Non-wetting phenomenon:
  • Adhesive force < cohesive force.
  • Angle of contact is more than π/2.

Capillary

• Height of liquid in capillary tube is given by:
  • Where, σ is surface tension of liquid and tube, θ is angle of contact, and d is diameter of capillary tube.